1. Technical Field
The present disclosure relates to a MEMS (Micro Electro Mechanical System) resonant accelerometer having improved electrical characteristics.
2. Description of the Related Art
As is known, MEMS accelerometers play an important role in the field of sensors with applications in various contexts including automotive, vibration monitoring and portable electronics. The large number of micro-accelerometers proposed in the literature and nowadays present on the market can be grouped in three classes, on the basis of the sensing principle: capacitive, resonant and piezoresistive. The more common surface micromachined accelerometers belong to the first class, but also resonant accelerometers have been produced by surface micromachining technology. In this respect, reference may be made to the following papers:    M. Aikele, K. Bauer, W. Ficker, F. Neubauer, U. Prechtel, J. Schalk, H. Seidel “Resonant accelerometer with self-test”, Sensors and Actuators A, 92, 161-167, 2001;    A. A. Seshia, M. Palaniapan, T. A. Roessig, R. T. Howe, R. W. Gooch, T. R. Shimert, S. Montague “A vacuum packaged surface micromachined resonant accelerometer”, JMEMS, 11, 784-793, 2002;    L. He; Y.-P. Xu; A. Qiu “Folded silicon resonant accelerometer with temperature compensation”, Sensors 2004. Proceedings of IEEE, 1, 512-515, 24-27 Oct. 2004;    S. X. P. Su, H. S. Yang, A. M. Agogino “A resonant accelerometer with two-stage microleverage mechanisms fabricated by SOI-MEMS technology” Sensors, 5(6), 1214-1223, 2005.
In resonant accelerometers, the external acceleration produces a recordable shift of the resonance frequency of the structure, or of some part thereof. Resonant sensing, with respect to other sensing principles, has the advantage of direct frequency output, high potential sensitivity and large dynamic range.
Sensitivity of resonant accelerometers is generally defined as the frequency shift produced by an external acceleration of 1 g. Known resonant accelerometers obtained through surface micromachining typically have sensitivity ranging from 40 Hz/g up to 160 Hz/g, and, at least some of them, have quite large dimensions.
A conceptual diagram of a linear accelerometer is shown in FIG. 1. An inertial mass m is attached to a frame by means of a spring of stiffness k and is subject to damping from the surrounding environment, represented by a damper of coefficient b. When the reference frame is subject to an external acceleration a, the oscillation of the inertial mass is governed by the dynamic equilibrium equation:m{umlaut over (x)}+b{dot over (x)}+kx=ma 
If the frequency Ω of the external acceleration is well below resonance, i.e., if Ω<<ω, ω=√{square root over (k/m)} being the frequency of the accelerometer, the accelerometer response is quasi-static and x(t)≈(m/k)a(t). The external acceleration turns out to be proportional to the mass displacement and sensing can be done by measuring the mass displacement, e.g., via the capacity variation as in known capacitive accelerometers.
In resonant accelerometers, instead, the input acceleration is detected in terms of a shift in the resonant frequency of a sensing device coupled to the proof mass. The corresponding scheme is represented in FIG. 2, where a resonating beam, shown horizontally, is the above sensing device.
The operating principle is based on the dependence of the resonant characteristic on the axial force which acts on the resonator. The external acceleration a produces a force, F=ma on the inertial mass m. This force produces, in turn, an axial force N in the resonating beam (which is driven in resonance). For a single span beam, frequency increases in the case of a tensile load and decreases in the case of a compressive load.
As is known, denoting by f0, the fundamental frequency of the beam resonating without axial load, the resonant frequency f of the axially loaded beam can be expressed as:
                    f        =                              f            0                    ⁢                                    1              +                              α                ⁢                                                      NL                    2                                    EI                                                                                        (        1        )            wherein:
                              f          0                =                                            c              2                                      2              ⁢              π              ⁢                                                          ⁢                              L                2                                              ⁢                                    EI                              ρ                ⁢                                                                  ⁢                A                                                                        (        2        )            and L, A and I are the length, the cross area and the inertial moment of the resonator, respectively, E is the elastic modulus, and c and α are coefficients depending on the boundary conditions of the resonator. The following table shows the values of these coefficients for several boundary conditions:
cαclamped-free1.8750.376sliding-pinned1.5720.405pinned-pinned3.1420.101sliding-sliding3.1420.101clamped-clamped4.7300.0246
As a general rule, the external acceleration and resulting force on the resonators produces a variation in the natural frequency of the same resonators and by measuring this frequency variation it is possible to obtain the value of the external acceleration.
Several accelerometers based on the resonant operating principle have been manufactured, through “bulk micromachining” and “surface micromachining” technologies. These known accelerometers have different geometry (in particular different arrangements of the resonating beam with respect to the proof or sensing mass) which greatly affect the amplification of the axial force and hence the sensitivity of the resulting sensor.
None of the proposed sensing structures has proven to be fully satisfactory in terms of the dimensions and electrical characteristics of the resulting accelerometer sensors. In particular, sensitivities limited to the range 10-160 Hz/g have been obtained with the known sensing structures having comparable size.